熟悉 NumPy 常用函数

# 来源：NumPy Biginner's Guide 2e ch3

读写文件

import numpy as np# eye 用于创建单位矩阵i2 = np.eye(2)print i2'''[[ 1.  0.][ 0.  1.]]'''# 将数组以纯文本保存到 eye.txt 中np.savetxt("eye.txt", i2)'''eye.txt:1.000000000000000000e+00 0.000000000000000000e+000.000000000000000000e+00 1.000000000000000000e+00'''# 还可以读进来print np.loadtxt('eye.txt')[[ 1.  0.] [ 0.  1.]]

读取 CSV

'''data.csv:AAPL,28-01-2011, ,344.17,344.4,333.53,336.1,21144800分别为：名称，日期，空，开盘，最高，最低，收盘，成交量'''# delimiter 是分隔符，设置为 ','# usecols 设置需要取的列，这里只选择了收盘和成交量# unpack 设置为 True，返回的数组是以列为主# 可以分别将收盘和成交量赋给 c 和 vc, v = np.loadtxt('data.csv', delimiter=',', usecols=(6,7), unpack=True)

均值

import numpy as npc, v = np.loadtxt('data.csv', delimiter=',', usecols=(6,7), unpack=True)# 计算成交量加权均价# average 用于计算均值# weights 参数指定权重vwap = np.average(c, weights=v)print "VWAP =", vwap# VWAP = 350.589549353# mean 函数也能用于计算均值print "mean =", np.mean(c)# mean =  351.037666667# 计算时间时间加权均价t = np.arange(len(c))print "twap =", np.average(c, weights=t)# twap = 352.428321839

最大最小值

import numpy as np# 这次读入了最高价和最低价h, l = np.loadtxt('data.csv', delimiter=',', usecols=(4,5), unpack=True)# 计算历史最高价和最低价print "highest =", np.max(h)# highest = 364.9print "lowest =", np.min(l)# lowest = 333.53# ptp 函数用于计算极差print "Spread high price", np.ptp(h)# Spread high price 24.86print "Spread low price", np.ptp(l)# Spread low price 26.97

简单统计

import numpy as np# 读入收盘价c = np.loadtxt('data.csv', delimiter=',', usecols=(6,), unpack=True)# 计算中位数print "median =", np.median(c)# median = 352.055# 手动计算中位数# 首先排个序sorted_close = np.msort(c)print "sorted =", sorted_close# 然后取中间元素N = len(c)print "middle =", sorted[(N - 1)/2]# middle = 351.99# 由于我们的数组长度是偶数# 中位数应该是中间两个数的均值# print "average middle =", (sorted[N /2] + sorted[(N - 1) / 2]) / 2# average middle = 352.055# 方差print "variance =", np.var(c)# variance = 50.1265178889# 手动计算方差print "variance from definition =", np.mean((c - c.mean())**2)# variance from definition = 50.1265178889

股票收益

import numpy as np# 简单收益# 当天收盘价减去前一天收盘价，再除以前一天收盘价# returns = np.diff( arr ) / arr[ : -1]# 我们计算一下标准差（方差的平方根）print "Standard deviation =", np.std(returns)# Standard deviation = 0.0129221344368# 对数收益# 当天收盘价的对数前前一天收盘价的对数logreturns = np.diff( np.log(c) )# 计算收益为正的下标# where 将布尔索引变成位置索引posretindices = np.where(returns > 0)print "Indices with positive returns", posretindices# Indices with positive returns (array([ 0,  1,  4,  5,  6,  7,  9, 10, 11, 12, 16, 17, 18, 19, 21, 22, 23, 25, 28]),)# 年化波动annual_volatility = np.std(logreturns)/np.mean(logreturns)annual_volatility = annual_volatility / np.sqrt(1./252.) print annual_volatility# 月化波动print "Monthly volatility", annual_volatility * np.sqrt(1./12.)

处理日期

import numpy as npfrom datetime import datetime# 将日期映射为星期# Monday 0# Tuesday 1# Wednesday 2# Thursday 3# Friday 4# Saturday 5# Sunday 6def datestr2num(s):    return datetime.strptime(s, "%d-%m-%Y").date().weekday()# 读取星期和收盘价，converters 将日期映射成星期dates, close = np.loadtxt('data.csv', delimiter=',', usecols=(1,6), converters={1: datestr2num}, unpack=True)print "Dates =", dates# Dates = [ 4.  0.  1.  2.  3.  4.  0.  1.  2.  3.  4.  0.  1.  2.  3.  4.  1.  2.  4.  0.  1.  2.  3.  4.  0.  1.  2.  3.  4.]# 计算一周中每一天的均值averages = np.zeros(5)for i in range(5):    indices = np.where(dates == i)     prices = np.take(close, indices)    avg = np.mean(prices)    print "Day", i, "prices", prices, "Average", avg    averages[i] = avg'''Day 0 prices [[ 339.32  351.88  359.18  353.21  355.36]] Average 351.79Day 1 prices [[ 345.03  355.2   359.9   338.61  349.31  355.76]] Average 350.635Day 2 prices [[ 344.32  358.16  363.13  342.62  352.12  352.47]] Average 352.136666667Day 3 prices [[ 343.44  354.54  358.3   342.88  359.56  346.67]] Average 350.898333333Day 4 prices [[ 336.1   346.5   356.85  350.56  348.16  360.    351.99]] Average 350.022857143'''# 计算星期几最高，星期几最低top = np.max(averages)print "Highest average", top# Highest average 352.136666667print "Top day of the week", np.argmax(averages)# Top day of the week 2bottom = np.min(averages)print "Lowest average", bottom# Lowest average 350.022857143print "Bottom day of the week", np.argmin(averages# Bottom day of the week 4

真实波动幅度均值（ATR）

# 真实波动幅度（TR）定义为以下三个度量的最大值# 1. 当天最高价减当天最低价# 2. 当天最高价减前一天的收盘价的绝对值# 3. 前一天收盘价减当天最低价的绝对值import numpy as npimport sys# 读入最高价、最低价、收盘价h, l, c = np.loadtxt('data.csv', delimiter=',', usecols=(4, 5, 6), unpack=True)# 读入数据数量N = int(sys.argv[1])# 获取最近 N 天的最高价和最低价h = h[-N:]l = l[-N:]print "len(h)", len(h), "len(l)", len(l)print "Close", c# 由于需要前一天的收盘价，所以往天移动一天previousclose = c[-N -1: -1]print "len(previousclose)", len(previousclose)print "Previous close", previousclose# maximum 逐元素获得最大值truerange = np.maximum(h - l, h - previousclose, previousclose - l) print "True range", truerange# 计算 ATRatr = np.zeros(N)# 第一个 ATR 通过均值来计算atr[0] = np.mean(truerange)# 计算之后每一个 ATR# atr[i] = ((N - 1) * atr[i - 1] + tr[i]) / Nfor i in range(1, N):   atr[i] = (N - 1) * atr[i - 1] + truerange[i]   atr[i] /= Nprint "ATR", atr

简单滑动均值

# 每一天的简单滑动均值# 就是当天与前 (N - 1) 天的均值# 其中 N 是窗口大小import numpy as npimport sysfrom matplotlib.pyplot import plotfrom matplotlib.pyplot import showN = int(sys.argv[1])# 使用 ones 函数创建大小为 N 的数组# 并除以 N 来创建权重weights = np.ones(N) / Nprint "Weights", weights# 假设 N 为 5：# Weights [ 0.2  0.2  0.2  0.2  0.2]# 读入收盘价c = np.loadtxt('data.csv', delimiter=',', usecols=(6,), unpack=True)# 调用 convolve 函数来计算滑动平均sma = np.convolve(weights, c)[N-1:-N+1]# 绘制函数图像# 要注意横轴从 (N - 1) 开始t = np.arange(N - 1, len(c))plot(t, c[N-1:], lw=1.0)plot(t, sma, lw=2.0)show()

注：

np.convolve计算离散卷积，定义为：

离散卷积其实就是系数数组的多项式乘法。例如计算[1, 2, 0, 3]和[1, -2, 5]的卷积：

结果为[1, 1, 13, -6, 15]。

指数滑动均值

import numpy as npimport sysfrom matplotlib.pyplot import plotfrom matplotlib.pyplot import showx = np.arange(5)# exp 计算 e 的 x 次方print "Exp", np.exp(x)# Exp [  1.           2.71828183   7.3890561   20.08553692  54.59815003]# linspace 使用起始值、终止值和数量，返回等间隔的数组print "Linspace", np.linspace(-1, 0, 5)# Linspace [-1.   -0.75 -0.5  -0.25  0.  ]N = int(sys.argv[1])# 计算权重weights = np.exp(np.linspace(-1., 0., N))weights /= weights.sum()print "Weights", weights# 假设 N 为 5：# Weights [ 0.11405072  0.14644403  0.18803785  0.24144538  0.31002201]# 读入收盘价c = np.loadtxt('data.csv', delimiter=',', usecols=(6,), unpack=True)# 使用 convolve 计算指数滑动均值ema = np.convolve(weights, c)[N-1:-N+1]# 绘制函数图像t = np.arange(N - 1, len(c))plot(t, c[N-1:], lw=1.0)plot(t, ema, lw=2.0)show()

布林带

import numpy as npimport sysfrom matplotlib.pyplot import plotfrom matplotlib.pyplot import show# 读取窗口大小N = int(sys.argv[1])# 这是简单滑动平均的权重weights = np.ones(N) / Nprint "Weights", weights# 读取收盘价c = np.loadtxt('data.csv', delimiter=',', usecols=(6,), unpack=True)# 计算简单滑动平均sma = np.convolve(weights, c)[N-1:-N+1]# 手动计算滑动标准差deviation = []C = len(c)for i in range(N - 1, C):    # 对于每一天    # 滑动标准差是当天与前 (N - 1) 天的标准差    # 和滑动均值类似，原书这里有误    dev = c[i - (N - 1): i + 1]    averages = np.zeros(N)    # 这里的 fill 将数组元素全部变为指定值    # 相当于 averages.flat = sma[i - (N - 1)]    # 但是比它快    averages.fill(sma[i - (N - 1)])    # 也可以直接写 dev -= sma[i - (N - 1)]    dev = dev - averages     dev = dev ** 2    dev = np.sqrt(np.mean(dev))    deviation.append(dev)deviation = 2 * np.array(deviation)print len(deviation), len(sma)# 上布林带是简单滑动均值加上两倍滑动标准差# 下布林带是简单滑动均值减去两倍滑动标准差upperBB = sma + deviationlowerBB = sma - deviationc_slice = c[N-1:]between_bands = np.where((c_slice < upperBB) & (c_slice > lowerBB))print lowerBB[between_bands]print c[between_bands]print upperBB[between_bands]between_bands = len(np.ravel(between_bands))print "Ratio between bands", float(between_bands)/len(c_slice)# 绘制收盘价、简单滑动均值# 上布林带和下布林带的图像# 要注意横轴从 N - 1 开始t = np.arange(N - 1, C)plot(t, c_slice, lw=1.0)plot(t, sma, lw=2.0)plot(t, upperBB, lw=3.0)plot(t, lowerBB, lw=4.0)show()

使用线性模型预测收盘价

import numpy as npimport sysN = int(sys.argv[1])# 读入收盘价c = np.loadtxt('data.csv', delimiter=',', usecols=(6,), unpack=True)# 取后 N 天的收盘价，并倒序b = c[-N:]bbx = b[::-1]print "bbx", bbx# bbx [ 351.99  346.67  352.47  355.76  355.36]# 构建 NxN 的二维数组A = np.zeros((N, N), float)print "Zeros N by N", A'''A = np.zeros((N, N), float)print "Zeros N by N", AZeros N by N [[ 0.  0.  0.  0.  0.] [ 0.  0.  0.  0.  0.] [ 0.  0.  0.  0.  0.] [ 0.  0.  0.  0.  0.] [ 0.  0.  0.  0.  0.]]'''# A[i] 是倒数第 i 天的前 N 天的收盘价for i in range(N):   A[i, ] = c[-N - 1 - i: - 1 - i]print "A", A'''A [[ 360.    355.36  355.76  352.47  346.67] [ 359.56  360.    355.36  355.76  352.47] [ 352.12  359.56  360.    355.36  355.76] [ 349.31  352.12  359.56  360.    355.36] [ 353.21  349.31  352.12  359.56  360.  ]]'''# 根据每一天前 N 天收盘价来预测当天收盘价# np.linalg.lstsq 是最小二乘法的多元线性回归# A 是输入属性的数据集，行是记录，列是属性# b 是输出属性的数组# x 是系数数组，x = (A^T A)^(-1) A^T b(x, residuals, rank, s) = np.linalg.lstsq(A, b)print x, residuals, rank, s# [ 0.78111069 -1.44411737  1.63563225 -0.89905126  0.92009049] [] 5 [  1.77736601e+03   1.49622969e+01   8.75528492e+00   5.15099261e+00   1.75199608e+00]# 通过后 N 天收盘价来预测下一天的收盘价print np.dot(b, x)# 357.939161015

剪切和压缩数组

import numpy as npa = np.arange(5)print "a =", a# a = [0 1 2 3 4]# clip 用于剪切数组# 小于最小值的元素会替换成最小值# 大于最大值的元素会替换成最大值print "Clipped", a.clip(1, 2)# Clipped [1 1 2 2 2]a = np.arange(4)print a# [0 1 2 3]# compress 用于过滤元素# 等价于 a[a > 2]print "Compressed", a.compress(a > 2)# Compressed [3]

计算阶乘

import numpy as npb = np.arange(1, 9)print "b =", b# b = [1 2 3 4 5 6 7 8]# prod 用于求出各元素乘积print "Factorial", b.prod()# Factorial 40320# cumprod 求出累积连乘# P[i] = a[0] * ... * a[i]print "Factorials", b.cumprod()# Factorials [    1     2     6    24   120   720  5040 40320]